A symmetric design with parameters (v,k,λ) is an incidence structure consisting of a set of v points and a set of v blocks with an incidence relation such that every block is incident with exactly k points, and each pair of points is incident with exactly λ blocks. An automorphism group of a symmetric design is a group of permutations on points of the design which maps blocks to blocks and preserves the incidence and non-incidence. The main part of this talk is devoted to giving a survey on recent study of symmetric designs which admit a group of automorphisms acting on the set of points and the set of blocks as well as the set of flags. We are in particular interested in automorphism groups acting primitively on the set of points.
